They're partly why I got into video games. Myst, King's Quest, Phantasmagoria, Journeyman Project, Siberia, you name it.
And another thing - is the new RPG-ish Bioware-pioneered cinematic-game genre actually the New "adventure" game?
I wouldn't exactly call it the new adventure game. It's been a popular template for the last 5 years or so, but it hasn't seen many clones as of yet. Alpha Protocol and Rise of the Argonauts are the only ones I can recall that tried to repeat it.
Would you hope for more ambient and indie-ish RPG/adventure games?
Outside of BioWare, you mean? They're already out there, you just have to look in the right places. Bastion, for one.
Would Bioware possibly be interested in less shooting, more ambience/art + pure story?
Well, they're a bit busy finishing off the ME trilogy, Designing Dragon Age III, Launching TOR, working on the new IP, and probably quite a bit more. I personally wouldn't expect it, but it's not completely out of question. Most people think "TeH RPG!!!" with BioWare, but they've done plenty out of that genre - Shattered Steel, MDK2, and whatever the new IP happens to be.